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The optimal strategy in this case is known and is called the Zallager curve. See http://www.wardsattic.com/joomla/Download/WebPresentation/zalgaller_escapes.ht
by btilly 8y ago
The optimal strategy in this case is known and is called the Zallager curve. See http://www.wardsattic.com/joomla/Download/WebPresentation/zalgaller_escapes.htm http://www.wardsattic.com/joomla/Download/WebPresentation/za... for a picture.
- saagarjha 8y agoSo you’re not too far off: the optimal value is 2.27.
- deleted 8y ago[deleted]
- dunkelheit 8y agoApparently you've mistyped the name - the curve is named after a Russian-Israeli mathematician Viktor Zalgaller.
- rocqua 8y agoWhat happens for a 1 : 1.1 rectangle? it seems to me that that curve isn't optimal then. If so, what is the ratio for a rectangle where that curve becomes optimal.
- pwiecz 8y agoIf I'm reading http://wardsattic.com/joomla/Download/BellmanForestProblem.pdf http://wardsattic.com/joomla/Download/BellmanForestProblem.p... correctly, the ratio you're looking for is ≈ 2.0471.
- rocqua 8y agothanks for the link!
- gvb 8y agoThat paper shows the value of visualization... I followed the Bellman Forest Problem link to the Wikipedia page on the Moser's Worm Problem[1] and it didn't do anything for me. In Ward's paper, he summarized Moser's Worm Problem differently (p.7): In 1966, Moser posed a related problem which roughly asks: “What's the best-shaped hammer for smashing one-inch worms?” Great visualization! [1] https://en.wikipedia.org/wiki/Moser%27s_worm_problem https://en.wikipedia.org/wiki/Moser%27s_worm_problem